Momentum, friction and acceleration in a small sized light weight robot
I have been working on a problem related to a robot that I am building. I am trying to find a formula to calculate the force needed to apply through motors to accelerate and turn the robot. The end goal of this task is to find a way to calculate the maximum force that a motor can apply on a specific moment without the wheels starting to slip on the ground. When I started to work on it I tried finding and describing the forces that affect the speed and momentum of it. I am currently stuck on the question of how the already moving robot with inertia affects the wheels. I have added a rough sketch of the robot to help visualize it.
My work so far:
Force applied by a motor: Force = torque / radius of a wheel
Internal friction of a DC motor: Force = coefficient * robot weight * gravity
I have understood that the internal friction changes with the speed that the motor is rotating, but I don't quite understand on how to measure or calculate it yet.
Wheel friction to the ground: Force = coefficient * robot weight * gravity
I am considering the effects of drag and wheel deformation to be irrelevantly small for the current situation.
I am still a bit unure on the effects of a centrifugal force in this situation, but I think the formula should look kinda like this: Friction of wheels sideways >= current speed of robot^2 / turning radius
Turning radius: Radius = disstance between wheels * (speed of wheel 1 + speed of wheel 2) / (2 * (speed of wheel 1  speed of wheel 2))
Any help and ideas are welcome
